Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition

Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyn'ska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The well-posedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.Comment: 6 pages, 0 figure

3D-electrical resistivity tomography monitoring of salt transport in homogeneous and layered soil samples

Monitoring transport of dissolved substances in soil deposits is particularly relevant where safety is concerned, as in the case of geo-environmental barriers. Geophysical methods are very appealing, since they cover a wide domain, localising possible preferential flow paths and providing reliable links between geophysical quantities and hydrological variables. This paper describes a 3D laboratory application of Electrical Resistivity Tomography (ERT) used to monitor solute transport processes. Dissolution and transport tests on both homogeneous and heterogeneous samples were conducted in an instrumented oedometer cell. ERT was used to create maps of electrical conductivity of the monitored domain at different time intervals and to estimate concentration variations within the interstitial fluid. Comparisons with finite element simulations of the transport processes were performed to check the consistency of the results. Tests confirmed that the technique can monitor salt transport, infer the hydro-chemical behaviour of heterogeneous geomaterials and evaluate the performances of clay barrier

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide-water flow in porous domain

This is the accepted version of the following article: DAS, D.B. ... et al., 2014. A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide-water flow in porous domain. AIChE Journal, 60 (12), pp. 4266-4278, which has been published in final form at http://dx.doi.org/10.1002/aic.14577Numerical simulations for core-scale capillary pressure (Pc)–saturation (S) relationships have been conducted for a supercritical carbon dioxide-water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO2. As the Pc-S relationships depend on both S and time derivative of saturation (∂S / ∂t) yielding what is known as the ‘dynamic capillary pressure effect’ or simply ‘dynamic effect’, this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide-water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO2-water flow is reached. The simulations in this work involved the solution of the extended version of Darcy’s law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried for 3D cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best-fit straight line plotted between (i) the differences in dynamic and equilibrium capillary pressures (Pc,dyn – Pc,equ) against (ii) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO2-water system increases as the saturation decreases. From a practical point view, it implies that the time to capillary equilibrium during geological sequestration of CO2 is an important factor and should be accounted for while simulating the flow processes, e.g., to determine the CO2 storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for supercritical CO2-water flow as well as τ values. These issues are addressed in this article